195 Search Results for "Liu, Yang"

Document
DOI: 10.4230/DagMan.11.1.19
Conversational Agents: A Framework for Evaluation (CAFE) (Dagstuhl Perspectives Workshop 24352)

Authors: Christine Bauer, Li Chen, Nicola Ferro, Norbert Fuhr, Avishek Anand, Timo Breuer, Guglielmo Faggioli, Ophir Frieder, Hideo Joho, Jussi Karlgren, Johannes Kiesel, Bart P. Knijnenburg, Aldo Lipani, Lien Michiels, Andrea Papenmeier, Maria Soledad Pera, Mark Sanderson, Scott Sanner, Benno Stein, Johanne R. Trippas, Karin Verspoor, and Martijn C. Willemsen

Published in: Dagstuhl Manifestos, Volume 11, Issue 1 (2025)

Abstract
During the workshop, we deeply discussed what CONversational Information ACcess (CONIAC) is and its unique features, proposing a world model abstracting it, and defined the Conversational Agents Framework for Evaluation (CAFE) for the evaluation of CONIAC systems, consisting of six major components: 1) goals of the system’s stakeholders, 2) user tasks to be studied in the evaluation, 3) aspects of the users carrying out the tasks, 4) evaluation criteria to be considered, 5) evaluation methodology to be applied, and 6) measures for the quantitative criteria chosen.
Cite as

Christine Bauer, Li Chen, Nicola Ferro, Norbert Fuhr, Avishek Anand, Timo Breuer, Guglielmo Faggioli, Ophir Frieder, Hideo Joho, Jussi Karlgren, Johannes Kiesel, Bart P. Knijnenburg, Aldo Lipani, Lien Michiels, Andrea Papenmeier, Maria Soledad Pera, Mark Sanderson, Scott Sanner, Benno Stein, Johanne R. Trippas, Karin Verspoor, and Martijn C. Willemsen. Conversational Agents: A Framework for Evaluation (CAFE) (Dagstuhl Perspectives Workshop 24352). In Dagstuhl Manifestos, Volume 11, Issue 1, pp. 19-67, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{bauer_et_al:DagMan.11.1.19,
  author =	{Bauer, Christine and Chen, Li and Ferro, Nicola and Fuhr, Norbert and Anand, Avishek and Breuer, Timo and Faggioli, Guglielmo and Frieder, Ophir and Joho, Hideo and Karlgren, Jussi and Kiesel, Johannes and Knijnenburg, Bart P. and Lipani, Aldo and Michiels, Lien and Papenmeier, Andrea and Pera, Maria Soledad and Sanderson, Mark and Sanner, Scott and Stein, Benno and Trippas, Johanne R. and Verspoor, Karin and Willemsen, Martijn C.},
  title =	{{Conversational Agents: A Framework for Evaluation (CAFE) (Dagstuhl Perspectives Workshop 24352)}},
  pages =	{19--67},
  journal =	{Dagstuhl Manifestos},
  ISSN =	{2193-2433},
  year =	{2025},
  volume =	{11},
  number =	{1},
  editor =	{Bauer, Christine and Chen, Li and Ferro, Nicola and Fuhr, Norbert and Anand, Avishek and Breuer, Timo and Faggioli, Guglielmo and Frieder, Ophir and Joho, Hideo and Karlgren, Jussi and Kiesel, Johannes and Knijnenburg, Bart P. and Lipani, Aldo and Michiels, Lien and Papenmeier, Andrea and Pera, Maria Soledad and Sanderson, Mark and Sanner, Scott and Stein, Benno and Trippas, Johanne R. and Verspoor, Karin and Willemsen, Martijn C.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagMan.11.1.19},
  URN =		{urn:nbn:de:0030-drops-252722},
  doi =		{10.4230/DagMan.11.1.19},
  annote =	{Keywords: Conversational Agents, Evaluation, Information Access}
}
Document
Survey
DOI: 10.4230/TGDK.3.2.1
Resilience in Knowledge Graph Embeddings

Authors: Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo

Published in: TGDK, Volume 3, Issue 2 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 2

Abstract
In recent years, knowledge graphs have gained interest and witnessed widespread applications in various domains, such as information retrieval, question-answering, recommendation systems, amongst others. Large-scale knowledge graphs to this end have demonstrated their utility in effectively representing structured knowledge. To further facilitate the application of machine learning techniques, knowledge graph embedding models have been developed. Such models can transform entities and relationships within knowledge graphs into vectors. However, these embedding models often face challenges related to noise, missing information, distribution shift, adversarial attacks, etc. This can lead to sub-optimal embeddings and incorrect inferences, thereby negatively impacting downstream applications. While the existing literature has focused so far on adversarial attacks on KGE models, the challenges related to the other critical aspects remain unexplored. In this paper, we, first of all, give a unified definition of resilience, encompassing several factors such as generalisation, in-distribution generalization, distribution adaption, and robustness. After formalizing these concepts for machine learning in general, we define them in the context of knowledge graphs. To find the gap in the existing works on resilience in the context of knowledge graphs, we perform a systematic survey, taking into account all these aspects mentioned previously. Our survey results show that most of the existing works focus on a specific aspect of resilience, namely robustness. After categorizing such works based on their respective aspects of resilience, we discuss the challenges and future research directions.
Cite as

Arnab Sharma, N'Dah Jean Kouagou, and Axel-Cyrille Ngonga Ngomo. Resilience in Knowledge Graph Embeddings. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 2, pp. 1:1-1:38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{sharma_et_al:TGDK.3.2.1,
  author =	{Sharma, Arnab and Kouagou, N'Dah Jean and Ngomo, Axel-Cyrille Ngonga},
  title =	{{Resilience in Knowledge Graph Embeddings}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{1:1--1:38},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.2.1},
  URN =		{urn:nbn:de:0030-drops-248117},
  doi =		{10.4230/TGDK.3.2.1},
  annote =	{Keywords: Knowledge graphs, Resilience, Robustness}
}
Document
Research
DOI: 10.4230/TGDK.3.2.3
GraphRAG on Technical Documents - Impact of Knowledge Graph Schema

Authors: Henri Scaffidi, Melinda Hodkiewicz, Caitlin Woods, and Nicole Roocke

Published in: TGDK, Volume 3, Issue 2 (2025). Transactions on Graph Data and Knowledge, Volume 3, Issue 2

Abstract
Retrieval Augmented Generation (RAG) is seeing rapid adoption in industry to enable employees to query information captured in proprietary data for their organisation. In this work, we test the impact of domain-relevant knowledge graph schemas on the results of Microsoft’s GraphRAG pipeline. Our approach aims to address the poor quality of GraphRAG responses on technical reports rich in domain-specific terms. The use case involves technical reports about geology, chemistry and mineral processing published by the Minerals Research Institute of Western Australia (MRIWA). Four schemas are considered: a simple five-class minerals domain expert-developed schema, an expanded minerals domain schema, the Microsoft GraphRAG auto-generated schema, and a schema-less GraphRAG. These are compared to a conventional baseline RAG. Performance is evaluated using a scoring approach that accounts for the mix of correct, incorrect, additional, and missing content in RAG responses. The results show that the simple five-class minerals domain schema extracts approximately 10% more entities from the MRIWA reports than the other schema options. Additionally, both the five-class and the expanded eight-class minerals domain schemas produce the most factually correct answers and the fewest hallucinations. We attribute this to the minerals-specific schemas extracting more relevant, domain-specific information during the Indexing stage. As a result, the Query stage’s context window includes more high-value content. This contributes to the observed improvement in answer quality compared to the other pipelines. In contrast, pipelines with fewer domain-related entities in the KG retrieve less valuable information, leaving more room for irrelevant content in the context window. Baseline RAG responses were typically shorter, less complete, and contained more hallucinations compared to our GraphRAG pipelines. We provide a complete set of resources at https://github.com/nlp-tlp/GraphRAG-on-Minerals-Domain/tree/main. These resources include links to the MRIWA reports, a set of questions (from simple to challenging) along with domain-expert curated answers, schemas, and evaluations of the pipelines.
Cite as

Henri Scaffidi, Melinda Hodkiewicz, Caitlin Woods, and Nicole Roocke. GraphRAG on Technical Documents - Impact of Knowledge Graph Schema. In Transactions on Graph Data and Knowledge (TGDK), Volume 3, Issue 2, pp. 3:1-3:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@Article{scaffidi_et_al:TGDK.3.2.3,
  author =	{Scaffidi, Henri and Hodkiewicz, Melinda and Woods, Caitlin and Roocke, Nicole},
  title =	{{GraphRAG on Technical Documents - Impact of Knowledge Graph Schema}},
  journal =	{Transactions on Graph Data and Knowledge},
  pages =	{3:1--3:24},
  ISSN =	{2942-7517},
  year =	{2025},
  volume =	{3},
  number =	{2},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/TGDK.3.2.3},
  URN =		{urn:nbn:de:0030-drops-248131},
  doi =		{10.4230/TGDK.3.2.3},
  annote =	{Keywords: RAG, minerals, local search, global search, entity extraction, competency questions}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ESA.2025.2
Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk)

Authors: Monika Henzinger and Roodabeh Safavi

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We give an introduction into differential privacy in the dynamic setting, called the continual observation setting.
Cite as

Monika Henzinger and Roodabeh Safavi. Securing Dynamic Data: A Primer on Differentially Private Data Structures (Invited Talk). In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 2:1-2:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.2,
  author =	{Henzinger, Monika and Safavi, Roodabeh},
  title =	{{Securing Dynamic Data: A Primer on Differentially Private Data Structures}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{2:1--2:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.2},
  URN =		{urn:nbn:de:0030-drops-244702},
  doi =		{10.4230/LIPIcs.ESA.2025.2},
  annote =	{Keywords: Differential privacy, continual observation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.54
Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems

Authors: Bingbing Hu and Adam Polak

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Most of the known tight lower bounds for dynamic problems are based on the Online Boolean Matrix-Vector Multiplication (OMv) Hypothesis, which is not as well studied and understood as some more popular hypotheses in fine-grained complexity. It would be desirable to base hardness of dynamic problems on a more believable hypothesis. We propose analogues of the OMv Hypothesis for variants of matrix multiplication that are known to be harder than Boolean product in the offline setting, namely: equality, dominance, min-witness, min-max, and bounded monotone min-plus products. These hypotheses are a priori weaker assumptions than the standard (Boolean) OMv Hypothesis and yet we show that they are actually equivalent to it. This establishes the first such fine-grained equivalence class for dynamic problems.
Cite as

Bingbing Hu and Adam Polak. Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{hu_et_al:LIPIcs.ESA.2025.54,
  author =	{Hu, Bingbing and Polak, Adam},
  title =	{{Non-Boolean OMv: One More Reason to Believe Lower Bounds for Dynamic Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{54:1--54:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.54},
  URN =		{urn:nbn:de:0030-drops-245228},
  doi =		{10.4230/LIPIcs.ESA.2025.54},
  annote =	{Keywords: Fine-grained complexity, OMv hypothesis, reductions, equivalence class}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.55
Safe Sequences via Dominators in DAGs for Path-Covering Problems

Authors: Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A path-covering problem on a directed acyclic graph (DAG) requires finding a set of source-to-sink paths that cover all the nodes, all the arcs, or subsets thereof, and additionally they are optimal with respect to some function. In this paper we study safe sequences of nodes or arcs, namely sequences that appear in some path of every path cover of a DAG. We show that safe sequences admit a simple characterization via cutnodes. Moreover, we establish a connection between maximal safe sequences and leaf-to-root paths in the source- and sink-dominator trees of the DAG, which may be of independent interest in the extensive literature on dominators. With dominator trees, safe sequences admit an O(n)-size representation and a linear-time output-sensitive enumeration algorithm running in time O(m + o), where n and m are the number of nodes and arcs, respectively, and o is the total length of the maximal safe sequences. We then apply maximal safe sequences to simplify Integer Linear Programs (ILPs) for two path-covering problems, LeastSquares and MinPathError, which are at the core of RNA transcript assembly problems from bioinformatics. On various datasets, maximal safe sequences can be computed in under 0.1 seconds per graph, on average, and ILP solvers whose search space is reduced in this manner exhibit significant speed-ups. For example on graphs with a large width, average speed-ups are in the range 50-250× for MinPathError and in the range 80-350× for LeastSquares. Optimizing ILPs using safe sequences can thus become a fast building block of practical RNA transcript assembly tools, and more generally, of path-covering problems.
Cite as

Francisco Sena, Romeo Rizzi, and Alexandru I. Tomescu. Safe Sequences via Dominators in DAGs for Path-Covering Problems. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 55:1-55:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{sena_et_al:LIPIcs.ESA.2025.55,
  author =	{Sena, Francisco and Rizzi, Romeo and Tomescu, Alexandru I.},
  title =	{{Safe Sequences via Dominators in DAGs for Path-Covering Problems}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{55:1--55:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.55},
  URN =		{urn:nbn:de:0030-drops-245230},
  doi =		{10.4230/LIPIcs.ESA.2025.55},
  annote =	{Keywords: directed acyclic graph, path cover, dominator tree, integer linear programming, least squares, minimum path error}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.26
Faster Dynamic 2-Edge Connectivity in Directed Graphs

Authors: Loukas Georgiadis, Konstantinos Giannis, and Giuseppe F. Italiano

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Let G be a directed graph with n vertices and m edges. We present a deterministic algorithm that maintains the 2-edge-connected components of G under a sequence of m edge insertions, with a total running time of O(n² log n). This significantly improves upon the previous best bound of O(mn) for graphs that are not very sparse. After each insertion, our algorithm supports the following queries with asymptotically optimal efficiency: - Test in constant time whether two query vertices v and w are 2-edge-connected in G. - Report in O(n) time all the 2-edge-connected components of G. Our approach builds on the recent framework of Georgiadis, Italiano, and Kosinas [FOCS 2024] for computing the 3-edge-connected components of a directed graph in linear time, which leverages the minset-poset technique of Gabow [TALG 2016]. Additionally, we provide a deterministic decremental algorithm for maintaining 2-edge-connectivity in strongly connected directed graphs. Given a sequence of m edge deletions, our algorithm maintains the 2-edge-connected components in total time n^(2+o(1)), while supporting the same queries as the incremental algorithm. This result assumes that the edges of a fixed spanning tree of G and of its reverse graph G^R are not deleted. Previously, the best known bound for the decremental problem was O(mn log n), obtained by a randomized algorithm without restrictions on the deletions. In contrast to prior dynamic algorithms for 2-edge-connectivity in directed graphs, our method avoids the incremental computation of dominator trees, thereby circumventing the known conditional lower bound of Ω(mn).
Cite as

Loukas Georgiadis, Konstantinos Giannis, and Giuseppe F. Italiano. Faster Dynamic 2-Edge Connectivity in Directed Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 26:1-26:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{georgiadis_et_al:LIPIcs.ESA.2025.26,
  author =	{Georgiadis, Loukas and Giannis, Konstantinos and Italiano, Giuseppe F.},
  title =	{{Faster Dynamic 2-Edge Connectivity in Directed Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{26:1--26:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.26},
  URN =		{urn:nbn:de:0030-drops-244945},
  doi =		{10.4230/LIPIcs.ESA.2025.26},
  annote =	{Keywords: Connectivity, dynamic algorithms, directed graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.18
Efficiency of Learned Indexes on Genome Spectra

Authors: Md. Hasin Abrar, Paul Medvedev, and Giorgio Vinciguerra

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Data structures on a multiset of genomic k-mers are at the heart of many bioinformatic tools. As genomic datasets grow in scale, the efficiency of these data structures increasingly depends on how well they leverage the inherent patterns in the data. One recent and effective approach is the use of learned indexes that approximate the rank function of a multiset using a piecewise linear function with very few segments. However, theoretical worst-case analysis struggles to predict the practical performance of these indexes. We address this limitation by developing a novel measure of piecewise-linear approximability of the data, called CaPLa (Canonical Piecewise Linear approximability). CaPLa builds on the empirical observation that a power-law model often serves as a reasonable proxy for piecewise linear-approximability, while explicitly accounting for deviations from a true power-law fit. We prove basic properties of CaPLa and present an efficient algorithm to compute it. We then demonstrate that CaPLa can accurately predict space bounds for data structures on real data. Empirically, we analyze over 500 genomes through the lens of CaPLa, revealing that it varies widely across the tree of life and even within individual genomes. Finally, we study the robustness of CaPLa as a measure and the factors that make genomic k-mer multisets different from random ones.
Cite as

Md. Hasin Abrar, Paul Medvedev, and Giorgio Vinciguerra. Efficiency of Learned Indexes on Genome Spectra. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{abrar_et_al:LIPIcs.ESA.2025.18,
  author =	{Abrar, Md. Hasin and Medvedev, Paul and Vinciguerra, Giorgio},
  title =	{{Efficiency of Learned Indexes on Genome Spectra}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{18:1--18:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.18},
  URN =		{urn:nbn:de:0030-drops-244865},
  doi =		{10.4230/LIPIcs.ESA.2025.18},
  annote =	{Keywords: Genome spectra, piecewise linear approximation, learned index, k-mers}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.67
Compact Representation of Semilinear and Terrain-Like Graphs

Authors: Jean Cardinal and Yelena Yuditsky

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We consider the existence and construction of biclique covers of graphs, consisting of coverings of their edge sets by complete bipartite graphs. The size of such a cover is the sum of the sizes of the bicliques. Small-size biclique covers of graphs are ubiquitous in computational geometry, and have been shown to be useful compact representations of graphs. We give a brief survey of classical and recent results on biclique covers and their applications, and give new families of graphs having biclique covers of near-linear size. In particular, we show that semilinear graphs, whose edges are defined by linear relations in bounded dimensional space, always have biclique covers of size O(npolylog n). This generalizes many previously known results on special classes of graphs including interval graphs, permutation graphs, and graphs of bounded boxicity, but also new classes such as intersection graphs of L-shapes in the plane. It also directly implies the bounds for Zarankiewicz’s problem derived by Basit, Chernikov, Starchenko, Tao, and Tran (Forum Math. Sigma, 2021). We also consider capped graphs, also known as terrain-like graphs, defined as ordered graphs forbidding a certain ordered pattern on four vertices. Terrain-like graphs contain the induced subgraphs of terrain visibility graphs. We give an elementary proof that these graphs admit biclique partitions of size O(nlog³ n). This provides a simple combinatorial analogue of a classical result from Agarwal, Alon, Aronov, and Suri on polygon visibility graphs (Discrete Comput. Geom. 1994). Finally, we prove that there exists families of unit disk graphs on n vertices that do not admit biclique coverings of size o(n^{4/3}), showing that we are unlikely to improve on Szemerédi-Trotter type incidence bounds for higher-degree semialgebraic graphs.
Cite as

Jean Cardinal and Yelena Yuditsky. Compact Representation of Semilinear and Terrain-Like Graphs. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 67:1-67:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{cardinal_et_al:LIPIcs.ESA.2025.67,
  author =	{Cardinal, Jean and Yuditsky, Yelena},
  title =	{{Compact Representation of Semilinear and Terrain-Like Graphs}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{67:1--67:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.67},
  URN =		{urn:nbn:de:0030-drops-245359},
  doi =		{10.4230/LIPIcs.ESA.2025.67},
  annote =	{Keywords: Biclique covers, intersection graphs, visibility graphs, Zarankiewicz’s problem}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.68
Faster Algorithm for Second (s,t)-Mincut and Breaking Quadratic Barrier for Dual Edge Sensitivity for (s,t)-Mincut

Authors: Surender Baswana, Koustav Bhanja, and Anupam Roy

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Let G be a directed graph on n vertices and m edges. In this article, we study (s,t)-cuts of second minimum capacity and present the following algorithmic and graph-theoretic results. 1) Second (s,t)-mincut: Vazirani and Yannakakis [ICALP 1992] designed the first algorithm for computing an (s,t)-cut of second minimum capacity using {O}(n²) maximum (s,t)-flow computations. We present the following algorithm that improves the running time significantly. For directed integer-weighted graphs, there is an algorithm that can compute an (s,t)-cut of second minimum capacity using Õ(√n) maximum (s,t)-flow computations with high probability. To achieve this result, a close relationship of independent interest is established between (s,t)-cuts of second minimum capacity and global mincuts in directed weighted graphs. 2) Minimum+1 (s,t)-cuts: Minimum+1 (s,t)-cuts have been studied quite well recently [Baswana, Bhanja, and Pandey, ICALP 2022 & TALG 2023], which is a special case of second (s,t)-mincut. We present the following structural result and the first nontrivial algorithm for minimum+1 (s,t)-cuts. 3) Algorithm: For directed multi-graphs, we design an algorithm that, given any maximum (s,t)-flow, computes a minimum+1 (s,t)-cut, if it exists, in O(m) time. 4) Structure: The existing structures for storing and characterizing all minimum+1 (s,t)-cuts occupy {O}(mn) space [Baswana, Bhanja, and Pandey, TALG 2023]. For undirected multi-graphs, we design a directed acyclic graph (DAG) occupying only {O}(m) space that stores and characterizes all minimum+1 (s,t)-cuts. This matches the space bound of the widely-known DAG structure for all (s,t)-mincuts [Picard and Queyranne, Math. Prog. Studies 1980]. 5) Dual Edge Sensitivity Oracle: The study of minimum+1 (s,t)-cuts often turns out to be useful in designing dual edge sensitivity oracles - a compact data structure for efficiently reporting an (s,t)-mincut after insertion/failure of any given pair of query edges. It has been shown recently [Bhanja, ICALP 2025] that any dual edge sensitivity oracle for (s,t)-mincut in undirected multi-graphs must occupy Ω(n²) space in the worst-case irrespective of the query time. Interestingly, for undirected unweighted simple graphs, we break this quadratic barrier while achieving a non-trivial query time as follows. There is an O(n√n) space data structure that can report an (s,t)-mincut in O(min{m,n√n}) time after the insertion/failure of any given pair of query edges. To arrive at our results, as one of our key techniques, we establish interesting relationships between (s,t)-cuts of capacity (minimum+Δ), Δ ≥ 0, and maximum (s,t)-flow. We believe that these techniques and the graph-theoretic result in 2.(b) are of independent interest.
Cite as

Surender Baswana, Koustav Bhanja, and Anupam Roy. Faster Algorithm for Second (s,t)-Mincut and Breaking Quadratic Barrier for Dual Edge Sensitivity for (s,t)-Mincut. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 68:1-68:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{baswana_et_al:LIPIcs.ESA.2025.68,
  author =	{Baswana, Surender and Bhanja, Koustav and Roy, Anupam},
  title =	{{Faster Algorithm for Second (s,t)-Mincut and Breaking Quadratic Barrier for Dual Edge Sensitivity for (s,t)-Mincut}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{68:1--68:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.68},
  URN =		{urn:nbn:de:0030-drops-245369},
  doi =		{10.4230/LIPIcs.ESA.2025.68},
  annote =	{Keywords: mincut, second mincut, compact structure, fault tolerant, sensitivity oracle, dual edges, st mincut, global mincut, characterization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.107
Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts

Authors: Bernhard Haeupler, Yaowei Long, Thatchaphol Saranurak, and Shengzhe Wang

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We show the existence of length-constrained expander decomposition in directed graphs and undirected vertex-capacitated graphs. Previously, its existence was shown only in undirected edge-capacitated graphs [Bernhard Haeupler et al., 2022; Haeupler et al., 2024]. Along the way, we prove the multi-commodity maxflow-mincut theorems for length-constrained expansion in both directed and undirected vertex-capacitated graphs. Based on our decomposition, we build a length-constrained flow shortcut for undirected vertex-capacitated graphs, which roughly speaking is a set of edges and vertices added to the graph so that every multi-commodity flow demand can be routed with approximately the same vertex-congestion and length, but all flow paths only contain few edges. This generalizes the shortcut for undirected edge-capacitated graphs from [Bernhard Haeupler et al., 2024]. Length-constrained expander decomposition and flow shortcuts have been crucial in the recent algorithms in undirected edge-capacitated graphs [Bernhard Haeupler et al., 2024; Haeupler et al., 2024]. Our work thus serves as a foundation to generalize these concepts to directed and vertex-capacitated graphs.
Cite as

Bernhard Haeupler, Yaowei Long, Thatchaphol Saranurak, and Shengzhe Wang. Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 107:1-107:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{haeupler_et_al:LIPIcs.ESA.2025.107,
  author =	{Haeupler, Bernhard and Long, Yaowei and Saranurak, Thatchaphol and Wang, Shengzhe},
  title =	{{Length-Constrained Directed Expander Decomposition and Length-Constrained Vertex-Capacitated Flow Shortcuts}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{107:1--107:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.107},
  URN =		{urn:nbn:de:0030-drops-245765},
  doi =		{10.4230/LIPIcs.ESA.2025.107},
  annote =	{Keywords: Length-Constrained Expander, Expander Decomposition, Shortcut}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.113
Bootstrapping Dynamic APSP via Sparsification

Authors: Rasmus Kyng, Simon Meierhans, and Gernot Zöcklein

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
We give a simple algorithm for the dynamic approximate All-Pairs Shortest Paths (APSP) problem. Given a graph G = (V, E, l) with polynomially bounded edge lengths, our data structure processes |E| edge insertions and deletions in total time |E|^{1+o(1)} and provides query access to |E|^o(1)-approximate distances in time Õ(1) per query. We produce a data structure that mimics Thorup-Zwick distance oracles [Thorup and Zwick, 2005], but is dynamic and deterministic. Our algorithm selects a small number of pivot vertices. Then, for every other vertex, it reduces distance computation to maintaining distances to a small neighborhood around that vertex and to the nearest pivot. We maintain distances between pivots efficiently by representing them in a smaller graph and recursing. We maintain these smaller graphs by (a) reducing vertex count using the dynamic distance-preserving core graphs of Kyng-Meierhans-Probst Gutenberg [Kyng et al., 2024] in a black-box manner and (b) reducing edge-count using a dynamic spanner akin to Chen-Kyng-Liu-Meierhans-Probst Gutenberg [Chen et al., 2024]. Our dynamic spanner internally uses an APSP data structure. Choosing a large enough size reduction factor in the first step allows us to simultaneously bootstrap a spanner and a dynamic APSP data structure. Notably, our approach does not need expander graphs, an otherwise ubiquitous tool in derandomization.
Cite as

Rasmus Kyng, Simon Meierhans, and Gernot Zöcklein. Bootstrapping Dynamic APSP via Sparsification. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 113:1-113:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kyng_et_al:LIPIcs.ESA.2025.113,
  author =	{Kyng, Rasmus and Meierhans, Simon and Z\"{o}cklein, Gernot},
  title =	{{Bootstrapping Dynamic APSP via Sparsification}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{113:1--113:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.113},
  URN =		{urn:nbn:de:0030-drops-245826},
  doi =		{10.4230/LIPIcs.ESA.2025.113},
  annote =	{Keywords: Dynamic Graph Algorithms, Spanners, Vertex Sparsification, Bootstrapping}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.36
Efficient Contractions of Dynamic Graphs - With Applications

Authors: Monika Henzinger, Evangelos Kosinas, Robin Münk, and Harald Räcke

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
A non-trivial minimum cut (NMC) sparsifier is a multigraph Ĝ that preserves all non-trivial minimum cuts of a given undirected graph G. We introduce a flexible data structure for fully dynamic graphs that can efficiently provide an NMC sparsifier upon request at any point during the sequence of updates. We employ simple dynamic forest data structures to achieve a fast from-scratch construction of the sparsifier at query time. Based on the strength of the adversary and desired type of time bounds, the data structure comes with different guarantees. Specifically, let G be a fully dynamic simple graph with n vertices and minimum degree δ. Then our data structure supports an insertion/deletion of an edge to/from G in n^o(1) worst-case time. Furthermore, upon request, it can return w.h.p. an NMC sparsifier of G that has O(n/δ) vertices and O(n) edges, in Ô(n) time. The probabilistic guarantees hold against an adaptive adversary. Alternatively, the update and query times can be improved to Õ(1) and Õ(n) respectively, if amortized-time guarantees are sufficient, or if the adversary is oblivious. Throughout the paper, we use Õ to hide polylogarithmic factors and Ô to hide subpolynomial (i.e., n^o(1)) factors. We discuss two applications of our new data structure. First, it can be used to efficiently report a cactus representation of all minimum cuts of a fully dynamic simple graph. Building this cactus for the NMC sparsifier instead of the original graph allows for a construction time that is sublinear in the number of edges. Against an adaptive adversary, we can with high probability output the cactus representation in worst-case Ô(n) time. Second, our data structure allows us to efficiently compute the maximal k-edge-connected subgraphs of undirected simple graphs, by repeatedly applying a minimum cut algorithm on the NMC sparsifier. Specifically, we can compute with high probability the maximal k-edge-connected subgraphs of a simple graph with n vertices and m edges in Õ(m+n²/k) time. This improves the best known time bounds for k = Ω(n^{1/8}) and naturally extends to the case of fully dynamic graphs.
Cite as

Monika Henzinger, Evangelos Kosinas, Robin Münk, and Harald Räcke. Efficient Contractions of Dynamic Graphs - With Applications. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 36:1-36:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{henzinger_et_al:LIPIcs.ESA.2025.36,
  author =	{Henzinger, Monika and Kosinas, Evangelos and M\"{u}nk, Robin and R\"{a}cke, Harald},
  title =	{{Efficient Contractions of Dynamic Graphs - With Applications}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{36:1--36:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.36},
  URN =		{urn:nbn:de:0030-drops-245047},
  doi =		{10.4230/LIPIcs.ESA.2025.36},
  annote =	{Keywords: Graph Algorithms, Cut Sparsifiers, Dynamic Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2025.91
Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism

Authors: Laxman Dhulipala, Monika Henzinger, George Z. Li, Quanquan C. Liu, A. R. Sricharan, and Leqi Zhu

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Many differentially private and classical non-private graph algorithms rely crucially on determining whether some property of each vertex meets a threshold. For example, for the k-core decomposition problem, the classic peeling algorithm iteratively removes a vertex if its induced degree falls below a threshold. The sparse vector technique (SVT) is generally used to transform non-private threshold queries into private ones with only a small additive loss in accuracy. However, a naive application of SVT in the graph setting leads to an amplification of the error by a factor of n due to composition, as SVT is applied to every vertex. In this paper, we resolve this problem by formulating a novel generalized sparse vector technique which we call the Multidimensional AboveThreshold (MAT) Mechanism which generalizes SVT (applied to vectors with one dimension) to vectors with multiple dimensions. When applied to vectors with n dimensions, we solve a number of important graph problems with better bounds than previous work. Specifically, we apply our MAT mechanism to obtain a set of improved bounds for a variety of problems including k-core decomposition, densest subgraph, low out-degree ordering, and vertex coloring. We give a tight local edge differentially private (LEDP) algorithm for k-core decomposition that results in an approximation with O(ε^{-1} log n) additive error and no multiplicative error in O(n) rounds. We also give a new (2+η)-factor multiplicative, O(ε^{-1} log n) additive error algorithm in O(log² n) rounds for any constant η > 0. Both of these results are asymptotically tight against our new lower bound of Ω(log n) for any constant-factor approximation algorithm for k-core decomposition. Our new algorithms for k-core decomposition also directly lead to new algorithms for the related problems of densest subgraph and low out-degree ordering. Finally, we give novel LEDP differentially private defective coloring algorithms that use number of colors given in terms of the arboricity of the graph.
Cite as

Laxman Dhulipala, Monika Henzinger, George Z. Li, Quanquan C. Liu, A. R. Sricharan, and Leqi Zhu. Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 91:1-91:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{dhulipala_et_al:LIPIcs.ESA.2025.91,
  author =	{Dhulipala, Laxman and Henzinger, Monika and Li, George Z. and Liu, Quanquan C. and Sricharan, A. R. and Zhu, Leqi},
  title =	{{Near-Optimal Differentially Private Graph Algorithms via the Multidimensional AboveThreshold Mechanism}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{91:1--91:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2025.91},
  URN =		{urn:nbn:de:0030-drops-245601},
  doi =		{10.4230/LIPIcs.ESA.2025.91},
  annote =	{Keywords: differential privacy, abovethreshold, densest subgraph}
}
Document
DOI: 10.4230/LIPIcs.ITP.2025.14
Canonical for Automated Theorem Proving in Lean

Authors: Chase Norman and Jeremy Avigad

Published in: LIPIcs, Volume 352, 16th International Conference on Interactive Theorem Proving (ITP 2025)

Abstract
Canonical is a solver for type inhabitation in dependent type theory, that is, the problem of producing a term of a given type. We present a Lean tactic which invokes Canonical to generate proof terms and synthesize programs. The tactic supports higher-order and dependently-typed goals, structural recursion over indexed inductive types, and definitional equality. Canonical finds proofs for 84% of Natural Number Game problems in 51 seconds total.
Cite as

Chase Norman and Jeremy Avigad. Canonical for Automated Theorem Proving in Lean. In 16th International Conference on Interactive Theorem Proving (ITP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 352, pp. 14:1-14:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{norman_et_al:LIPIcs.ITP.2025.14,
  author =	{Norman, Chase and Avigad, Jeremy},
  title =	{{Canonical for Automated Theorem Proving in Lean}},
  booktitle =	{16th International Conference on Interactive Theorem Proving (ITP 2025)},
  pages =	{14:1--14:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-396-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{352},
  editor =	{Forster, Yannick and Keller, Chantal},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2025.14},
  URN =		{urn:nbn:de:0030-drops-246128},
  doi =		{10.4230/LIPIcs.ITP.2025.14},
  annote =	{Keywords: Automated Reasoning, Interactive Theorem Proving, Dependent Type Theory, Inhabitation, Unification, Program Synthesis, Formal Methods}
}
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